Reduce to lowest terms: $- \dfrac{8}{5} \div \dfrac{6}{7} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{6}{7}$ is $ \dfrac{7}{6}$ Therefore: $ - \dfrac{8}{5} \div \dfrac{6}{7} = - \dfrac{8}{5} \times \dfrac{7}{6} $ $ \phantom{- \dfrac{8}{5} \times \dfrac{7}{6}} = \dfrac{-8 \times 7}{5 \times 6} $ $ \phantom{- \dfrac{8}{5} \times \dfrac{7}{6}} = \dfrac{-56}{30} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-56}{30} = \dfrac{-56 \div 2}{30 \div 2} = -\dfrac{28}{15} $